Nathan Smith and Jamie Proctor scored seven minutes apart in the first half to stake the Valiants to a two-goal lead before Robert Milsom pulled one back for the Yellow Army in the 36th minute.
The hosts were level when Ben Garrity headed into his own net, but Port Vale went back in front through Tom Conlon and appeared on course to take all three points back to Burslem.
Will Randall equalized three minutes from time and Coby Rowe capped the classic with the match-winner in the first minute of stoppage time to send Sutton up to seventh in the EFL League Two table.
Story of the match
It was a cagey affair at the start with both teams looking to get on the front foot until the 21st minute mark when an inch-perfect cross was sent in by Proctor onto the head of Smith and he headed the ball over Dean Bouzanis to give Port Vale the lead.
A minute later, James Wilson tried his luck, but Bouzanis was equal to the task.
In the 28th minute, the advantage was doubled as James Gibbons beat his man and found Proctor completely unmarked in the area and he slotted the ball into the far bottom corner to make it 2-0.
The lead was halved when Milsom’s shot from outside the area was deflected and rolled into the opposite corner, squeezing inside the post despite Lucas Covolan's attempts to keep it out.
The visitors started the brighter of the two in the second half, a solo run from Wilson in the 48th minute after got him into the Sutton area but his shot was tame and straight at Bouzanis.
A controversial moment occurred in the 69th minute. Dan Jones flicked the ball against a Yellow Army defender for a throw-in but the referee gave the throw to the hosts.
The ball was launched into the area which bobbled around and ended up in Vale’s net off the head of Garrity from Milsom's cross. Three minutes later, Conlon won a header in the area which had Bouzanis scrambling across to get it.
After coming close with a header earlier, Conlon restored Port Vale's lead following a corner. The ball was cleared away into his path and he struck the ball from outside of the area on the half volley.
Richie Bennett nearly equalized immediately, but in the 87th minute, Ricky Korboa laid a cross back for Joe Kizzi whose cross found Randall in the area and he headed past Covolan to level at 3-3.
In stoppage time, George Lloyd went down and was judged to have fouled his man. Confusion on the pitch as all 20 outfield players went to one end of the pitch before the referee gave the decision the other way and all 20 marched down to the other end.
The ball was put in and after a goal-mouth scramble, Rowe smashed it into the net from close range to give Sutton a pulsating victory.
Man of the match: Coby Rowe
In a wild game that saw several outstanding performances, Rowe was alert enough to keep his composure and find the ball during the scramble at the end of the match and give Sutton all three points.